The problem asks us to find the market equilibrium point given the demand and supply functions: Demand: $p = -3q + 36$ Supply: $p = 4q + 1$ We need to find the equilibrium price $p$ and quantity $q$.

1. Problem Description

The problem asks us to find the market equilibrium point given the demand and supply functions:

Demand: $p = -3q + 36$

Supply: $p = 4q + 1$

We need to find the equilibrium price $p$ and quantity $q$.

2. Solution Steps

The market equilibrium occurs when the demand equals the supply. Therefore, we set the demand function equal to the supply function and solve for $q$.

$-3q + 36 = 4q + 1$

Adding $3q$ to both sides:

$36 = 7q + 1$

Subtracting 1 from both sides:

$35 = 7q$

Dividing by 7:

$q = \frac{35}{7}$

$q = 5$

Now that we have the equilibrium quantity $q$, we can substitute it into either the demand or supply function to find the equilibrium price $p$. We'll use the supply function:

$p = 4q + 1$

$p = 4(5) + 1$

$p = 20 + 1$

$p = 21$

We can check our answer using the demand function:

$p = -3q + 36$

$p = -3(5) + 36$

$p = -15 + 36$

$p = 21$

Both functions give the same price, so our solution is correct.

3. Final Answer

The market equilibrium point is $q=5$ and $p=21$.